On Tue, Jun 2, 2015 at 7:18 AM, Lawrence Mitchell < [email protected]> wrote:
> -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA1 > > On 02/06/15 13:14, Matthew Knepley wrote: > > On Tue, Jun 2, 2015 at 6:13 AM, Justin Chang <[email protected] > > <mailto:[email protected]>> wrote: > > > > In FEniCS's Stokes example (example 19), one defines the > > Taylor-Hood function spaces with these three lines: > > > > V = VectorFunctionSpace(mesh, "CG", 2) Q = FunctionSpace(mesh, > > "CG", 1) W = V * Q > > > > To implement P2/(P1+P0), all we gotta do is this: > > > > V = VectorFunctionSpace(mesh, "CG", 2) Q = FunctionSpace(mesh, > > "CG", 1) P = FunctionSpace(mesh, "DG", 0) W = V * (Q + P) > > > > > > So here you would need 4 dual basis vectors, which I am assuming > > are: > > > > ev_(-1, -1), ev_(1, -1), ev_(-1, 1), ev_(-0.5, -0.5) > > > > where ev_(x, y) is the point evaluation functional at (x, y). Then > > you need some basis for the primal space, which naively is > > > > 1, x, y, 1 > > > > As you can see, this basis in linearly dependent, so the > > Vandermonde matrix that FIAT constructs will be singular. The > > construction of a nodal basis will fail. > > > > So Jed's question is, what are they actually doing internally? > > So-called "enriched" elements in FEniCS are not created with a nodal > basis, instead te "basis" for the space Q + P is just the > concatenation of the bases for Q and P separately and so tabulation of > basis functions at points is just the concatentation of the tabulation > of Q and that of P. > This construction appears to throw away unisolvence. In the Boffi paper, they use QR to solve the pressure Laplacian. This would put a damper on me using the method. Justin, how do they solve the system in the FEniCS example? Thanks, Matt > Lawrence > > -----BEGIN PGP SIGNATURE----- > Version: GnuPG v1 > > iQEcBAEBAgAGBQJVbZ8UAAoJECOc1kQ8PEYvfMEH/RjoxiJLL/Jl7/FzZSZCgTVF > 2WodH3Xnt+vD6+L6IhbZ5g+R9F4leRHBnin8wRZKdE9GepbFIGpDRxq6ydhzqpUU > eyawpNWltsJ2JcxAJo6nUxACQYJyAVr8xrlkfg90OGTPT8CTvliZ8545j+cr2EGC > 80vtw2vZOx0WKJ3CFQ0RfbjSYnUf1UibV30WfSr8qm2IbysKxEBKUFC/JbXZ1vft > MIzbK8koA5Ix58vss3YUAr7aCOB39xy/2xokW5G+fzvocCPxr3Wkv+lST3f9yzLA > mXns+DJGzuAZJaX64ZnpS+n8yVzySECjLjeIecMB5rXTBwkiQUheTDVGhtifNrY= > =ZWA6 > -----END PGP SIGNATURE----- > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener
